The object of research is the inertia tensor of an autonomous mobile robot (AMR) with a manipulator with different configurations of their mutual position. As an example of the AMR design of a changing configuration, an all-wheel drive four-wheeled platform with a manipulator is considered, consisting of a docking disk rotating around a vertical axis and rod links of the arm connected by rotational kinematic pairs of the fifth class. The mass of moving structural elements, i. e., a manipulator with a load, is 10–20 % of the mass of the robot platform. Let’s consider that the links of the manipulator and the platform are absolutely rigid and homogeneous bodies with a constant density; let’s neglect the mass of kinematic pairs. The next step in the analysis of the AMR inertia tensor of a changing configuration can be a study taking into account the elastic properties of the manipulator links, the uneven distribution of the masses of the platform, and the characteristics of the kinematic pairs. The dependence of the values of the elements of the AMR inertia tensor of a changing configuration on the values of the generalized coordinates of the moving elements of the structure and the ratio of the mass of the platform and the mass of the moving elements of the structure has been studied. The analysis of the inertia tensor of the AMR with a manipulator at different configurations of their mutual position showed that the values of the centrifugal moments of inertia of the system during the relative motion of the manipulator are commensurate with the value of the axial moments of inertia of the system, even if the mass of the moving structural elements is less than 10% of the mass of the platform. In most existing AMRs, the mass of moving structural elements is up to 20% of the platform mass, therefore, in the general case, the inertia tensor of such a system should be taken as off-diagonal and non-stationary. In the future, this will make it possible to refine the equation of dynamics, take into account the relationship of control channels, simulate the movement of AMR of a changing configuration, and optimize energy costs. Since AMR with the manipulator is an example of the «changing AMR» object class, the results obtained can be applied to all objects of this class.

This paper considers the construction of a mathematical model of the movement of an autonomous mobile robot (AMR) in variable configuration, taking into account the relationship of the dynamic parameters of a mechanical system. As an example, the design of AMR with a manipulator is considered. The object of this study is the dynamics of AMR with a manipulator. The peculiarities of the dynamics of AMR with the manipulator are due to the change in the position of the center of mass of the system with the relative movement of the manipulator and the commensurate non-diagonal and diagonal elements of the inertia tensor calculated relative to the axes of the base coordinate system. The construction of the mathematical model was carried out according to the Nyton-Euler method. The resulting mathematical model contains: – an equation of motion of the center of mass of the AMR system of variable configuration along the trajectory in the inertial coordinate system; – an equation of angular motion of AMR in variable configuration in the inertial coordinate system; – an equation of motion of the manipulator with respect to AMR. In a general case, the center of mass of the AMR platform moves in a horizontal plane. Establishing the relationship of dynamic parameters of the mechanical system will make it possible to maintain functionality and ensure the orientation of AMR in vertical planes despite the movement of the manipulator. As an object of control, AMR with a manipulator is a multi-connected system with a cross-internal connection of control channels, which is formed by the dynamic parameters of a mechanical system. Based on the results of mathematical modeling using the proposed model, it is possible to develop algorithms for adaptive control using cross-connection of channels. This will make it possible to identify reserves to reduce energy consumption, increase stability, improve the efficiency and survivability of AMR in variable configuration during autonomous work under extreme conditions.

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This paper has proposed a program analysis method over the current state of the workspace of an anthropomorphic manipulator using the Mathcad software application package (USA). The analysis of the manipulator workspace helped solve the following sub-tasks: to calculate the limits of the grip reach, to determine the presence of "dead zones" within the manipulator workspace, to build the boundaries of the manipulator workspace. A kinematic scheme of the manipulator typically provides for at least five degrees of mobility, which is why in the three-dimensional Cartesian coordinate system the work zone boundaries represent the surfaces of a complex geometric shape. The author-devised method makes it possible to construct the projections of the boundaries of the manipulator's work zone onto the coordinate planes in the frame of reference associated with the base of the robot. Using Mathcad's built-in features makes it possible to effectively solve the above sub-tasks without wasting time developing specialized software. The Mathcad software application package provides for the possibility of a symbolic solution to the first problem of the kinematics of an industrial robot, that is, the program generates analytical dependences of the coordinates for special point P (pole) of the grip on the trigonometrical functions of the generalized coordinates. The resulting analytical dependences are used for kinematic and dynamic analysis of the manipulator. Special features in constructing mathematical models when using the Mathcad software application package have been revealed. Simulating the manipulator movement taking into consideration constraints for kinematic pairs, the drives' power, as well as friction factors, makes it possible to optimize the parameters of the manipulator kinematic scheme. An example of the analysis of the working space of an anthropomorphic manipulator with five degrees of mobility has been considered. The reported results could be used during the design, implementation, modernization, and operation of manipulators.

A universal anthropomorphic manipulator with six rotational degrees of mobility is considered. The nodal points S0, ..., S6 are selected on the trajectory of movement of the manipulator grip. The kinematic analysis of the manipulator was carried out by the method of transforming the coordinates of Denavit - Hartenberg. The mathematical model of the manipulator is compiled by the Lagrange-Euler method. The problem of maximum performance for each generalized coordinate qi (t) is solved using the Pontryagin maximum principle. Mathematical modeling was carried out in the Mathcad environment. The software method for analyzing the speed of the manipulator allows us to consider for each nodal point of the trajectory S0, ..., S6 the set of admissible configurations of the manipulator, solve the problem of maximum speed for each generalized coordinate qi (t) and estimate the minimum time for the implementation of the sequence of state vectors. When solving the problem of maximum speed, the switching time ti1 and the minimum turning time tik are calculated for each generalized coordinate qi (t). The minimum time for the configuration implementation can be found by summing the minimum rotation time tik over six generalized coordinates. Similar calculations are carried out for each nodal point S0, ..., S6 and the corresponding sets of permissible manipulator configurations. The developed software makes it possible, on the basis of the data obtained, to synthesize a sequence of control commands for the manipulator drives. The research results can be used at the design stage, implementation and modernization of robotic systems and manipulators.